hw4
Tergelsaran Enkhbold
2023-05-24
library(ISLR2)## Warning: package 'ISLR2' was built under R version 4.2.3Weekly = na.omit(Weekly)
head(Weekly) ## Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today Direction
## 1 1990 0.816 1.572 -3.936 -0.229 -3.484 0.1549760 -0.270 Down
## 2 1990 -0.270 0.816 1.572 -3.936 -0.229 0.1485740 -2.576 Down
## 3 1990 -2.576 -0.270 0.816 1.572 -3.936 0.1598375 3.514 Up
## 4 1990 3.514 -2.576 -0.270 0.816 1.572 0.1616300 0.712 Up
## 5 1990 0.712 3.514 -2.576 -0.270 0.816 0.1537280 1.178 Up
## 6 1990 1.178 0.712 3.514 -2.576 -0.270 0.1544440 -1.372 Down# Question a: The summary of the weekly data
# Numerical
summary(Weekly)## Year Lag1 Lag2 Lag3
## Min. :1990 Min. :-18.1950 Min. :-18.1950 Min. :-18.1950
## 1st Qu.:1995 1st Qu.: -1.1540 1st Qu.: -1.1540 1st Qu.: -1.1580
## Median :2000 Median : 0.2410 Median : 0.2410 Median : 0.2410
## Mean :2000 Mean : 0.1506 Mean : 0.1511 Mean : 0.1472
## 3rd Qu.:2005 3rd Qu.: 1.4050 3rd Qu.: 1.4090 3rd Qu.: 1.4090
## Max. :2010 Max. : 12.0260 Max. : 12.0260 Max. : 12.0260
## Lag4 Lag5 Volume Today
## Min. :-18.1950 Min. :-18.1950 Min. :0.08747 Min. :-18.1950
## 1st Qu.: -1.1580 1st Qu.: -1.1660 1st Qu.:0.33202 1st Qu.: -1.1540
## Median : 0.2380 Median : 0.2340 Median :1.00268 Median : 0.2410
## Mean : 0.1458 Mean : 0.1399 Mean :1.57462 Mean : 0.1499
## 3rd Qu.: 1.4090 3rd Qu.: 1.4050 3rd Qu.:2.05373 3rd Qu.: 1.4050
## Max. : 12.0260 Max. : 12.0260 Max. :9.32821 Max. : 12.0260
## Direction
## Down:484
## Up :605
##
##
##
## # Graphical
library(corrplot)## Warning: package 'corrplot' was built under R version 4.2.3## corrplot 0.92 loadedcorrplot(cor(Weekly[,-9]), method="square")
title("Summary")
# Training&testing
library(dplyr) ## Warning: package 'dplyr' was built under R version 4.2.3##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2) ## Warning: package 'ggplot2' was built under R version 4.2.3library(rsample)
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.2.3## Warning: package 'tibble' was built under R version 4.2.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ lubridate 1.9.2 ✔ tibble 3.2.1
## ✔ purrr 1.0.1 ✔ tidyr 1.3.0
## ✔ readr 2.1.4## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errorslibrary(caret) ## Warning: package 'caret' was built under R version 4.2.3## Loading required package: lattice
##
## Attaching package: 'caret'
##
## The following object is masked from 'package:purrr':
##
## liftlibrary(vip)## Warning: package 'vip' was built under R version 4.2.3##
## Attaching package: 'vip'
##
## The following object is masked from 'package:utils':
##
## vilibrary(kknn)## Warning: package 'kknn' was built under R version 4.2.3##
## Attaching package: 'kknn'
##
## The following object is masked from 'package:caret':
##
## contr.dummyset.seed(123)
week_split <- initial_split(Weekly, prop = .7, strata ="Direction")
week_train <- training(week_split)
head(week_train)## Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today Direction
## 2 1990 -0.270 0.816 1.572 -3.936 -0.229 0.148574 -2.576 Down
## 10 1990 1.253 0.041 0.807 -1.372 1.178 0.133635 -2.678 Down
## 11 1990 -2.678 1.253 0.041 0.807 -1.372 0.149024 -1.793 Down
## 17 1990 2.420 -0.017 0.750 4.022 2.820 0.172625 -1.225 Down
## 24 1990 -1.552 2.480 0.112 0.729 -2.061 0.166956 -2.259 Down
## 25 1990 -2.259 -1.552 2.480 0.112 0.729 0.171718 -2.428 Downweek_test <- testing(week_split)
head(week_test)## Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today Direction
## 1 1990 0.816 1.572 -3.936 -0.229 -3.484 0.1549760 -0.270 Down
## 3 1990 -2.576 -0.270 0.816 1.572 -3.936 0.1598375 3.514 Up
## 5 1990 0.712 3.514 -2.576 -0.270 0.816 0.1537280 1.178 Up
## 6 1990 1.178 0.712 3.514 -2.576 -0.270 0.1544440 -1.372 Down
## 8 1990 0.807 -1.372 1.178 0.712 3.514 0.1323100 0.041 Up
## 12 1990 -1.793 -2.678 1.253 0.041 0.807 0.1357900 2.820 Up``{r} # Question b: Use the full data set to perform a logistic regression with Direction as the response and the five lag variables plus Volume as predictors. Use the summary() function to print the results. Do any of the predictors appear to be statistically significant? If so,which ones?
model1 <-glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume, data=week_train,family=binomial)
summary(model1)##
## Call:
## glm(formula = Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 +
## Volume, family = binomial, data = week_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0820 -1.2486 0.9596 1.0805 1.5091
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.305306 0.102934 2.966 0.00302 **
## Lag1 -0.043377 0.030582 -1.418 0.15608
## Lag2 0.035335 0.030947 1.142 0.25354
## Lag3 0.004343 0.032683 0.133 0.89428
## Lag4 -0.002149 0.033088 -0.065 0.94822
## Lag5 -0.080433 0.033615 -2.393 0.01672 *
## Volume -0.042205 0.044740 -0.943 0.34552
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1045.5 on 760 degrees of freedom
## Residual deviance: 1034.7 on 754 degrees of freedom
## AIC: 1048.7
##
## Number of Fisher Scoring iterations: 4# Question c: Compute the confusion matrix and overall fraction of correct predictions. Explain what the confusion matrix is telling you about the types of mistakes made by logistic regression.
predicted1 <- predict(model1, week_train)
predicted2 <- if_else(predicted1 > 0.5, "Up", "Down")
cross.tab1 <-table(week_train$Direction, predicted2)
cross.tab1## predicted2
## Down Up
## Down 312 26
## Up 373 50# Question d: (d) Now fit the logistic regression model using a training data period from 1990 to 2008, with Lag2 as the only predictor. Compute the confusion matrix and the overall fraction of correct predictions for the held out data (that is, the data from 2009 and 2010).
names (Weekly)## [1] "Year" "Lag1" "Lag2" "Lag3" "Lag4" "Lag5"
## [7] "Volume" "Today" "Direction"summary(Weekly$Year)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1990 1995 2000 2000 2005 2010train = (Weekly$Year<2009)
weekly_test = Weekly[!train,]
Dir_test= Weekly$Direction[!train]
model2 <- glm(Direction~Lag2, data = Weekly, family = "binomial",
subset = train)
predicted3 <- predict(model2,weekly_test, type="response")
predicted4 = rep("Down", nrow(weekly_test))
predicted4[predicted3 > .5] = "Up"
table(predicted4, Dir_test)## Dir_test
## predicted4 Down Up
## Down 9 5
## Up 34 56# Question e: Repeat (d) using LDA
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## The following object is masked from 'package:ISLR2':
##
## Bostonmodel3 <- lda(Direction~Lag2, data = Weekly, family = "binomial",
subset = train)
model3## Call:
## lda(Direction ~ Lag2, data = Weekly, family = "binomial", subset = train)
##
## Prior probabilities of groups:
## Down Up
## 0.4477157 0.5522843
##
## Group means:
## Lag2
## Down -0.03568254
## Up 0.26036581
##
## Coefficients of linear discriminants:
## LD1
## Lag2 0.4414162predicted5 <- predict(model3, weekly_test)
predicted6 = predicted5$class
table(predicted6, Dir_test)## Dir_test
## predicted6 Down Up
## Down 9 5
## Up 34 56# Question f: Repeat (d) using QDA.
model4 <- qda(Direction~Lag2, data = Weekly, family = "binomial",
subset = train)
predicted7 <- predict(model4, weekly_test)
predicted8 = predicted7$class
table(predicted8, Dir_test)## Dir_test
## predicted8 Down Up
## Down 0 0
## Up 43 61# Question g: Repeat (d) using KNN with K = 1
train.X = as.matrix(Weekly$Lag2[train])
test.X = as.matrix(Weekly$Lag2[!train])
train.Direction = Weekly$Direction[train]
summary(Weekly$Direction[train])## Down Up
## 441 544library("naivebayes")## Warning: package 'naivebayes' was built under R version 4.2.3## naivebayes 0.9.7 loadedmodel6 <- naive_bayes(Direction ~ Lag1, data = Weekly, family = "binomial",
subset = train)
predicted10 <- predict(model6, weekly_test)## Warning: predict.naive_bayes(): more features in the newdata are provided as
## there are probability tables in the object. Calculation is performed based on
## features to be found in the tables.predicted11 <- if_else(predicted10 > 0.5, "Up", "Down")## Warning in Ops.factor(predicted10, 0.5): '>' not meaningful for factorscross.tab6 <-table(weekly_test$Direction, predicted11)
cross.tab6## < table of extent 2 x 0 >